Simplify; express your answer in exponential form. Assume $z\neq 0, a\neq 0$. $\dfrac{{z^{-4}}}{{z^{3}a^{3}}}$
Answer: To start, try working on the numerator and the denominator independently. In the numerator, we have ${z^{-4}}$ to the exponent ${1}$ . Now ${-4 \times 1 = -4}$ , so ${z^{-4} = z^{-4}}$ In the denominator, we can use the distributive property of exponents. ${z^{3}a^{3} = z^{3}a^{3}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{z^{-4}}}{{z^{3}a^{3}}} = \dfrac{{z^{-4}}}{{z^{3}a^{3}}}$ Break up the equation by variable and simplify. $\dfrac{{z^{-4}}}{{z^{3}a^{3}}} = \dfrac{{z^{-4}}}{{z^{3}}} \cdot \dfrac{{1}}{{a^{3}}} = z^{{-4} - {3}} \cdot a^{- {3}} = z^{-7}a^{-3}$.